文献中也称circle packing in a squarepacking equal circles in a unit squarecsq
在边长 1 的正方形内放置 n 个半径相同、互不重叠的圆，使共同半径尽可能大。
| 纪录 | 数值 / 区间 | 作者 / 持有人 | 来源 |
|---|---|---|---|
| 外部已知最好 | [0.0367716871715, 0.0367716871725] | 见来源署名 | packomania.com ↗ |
| 本站纪录 | 暂无选手纪录 | — | — |
当前展示：起步布局
最优构形是「卡死」的接触结构：圆彼此顶住、顶住边界，常出现斜排、错位、以及不碰任何邻居的游离圆。规整的网格摆法几乎从不最优。
n = 1–30 已证明最优，适合观察经典接触结构；n = 31–300 接入 Packomania 的公开前沿，除 n = 36 外最优性仍未知。大规模部分集中成一张表，供算法批量挑战。
查看来源
查看构型、求解笔记与纪录历史。
容器是边长 1 的正方形，左下角是原点 (0, 0)，右上角是 (1, 1)。坐标和长度用同一个单位，直接写成小数，例如 "0.5"，最多九位小数。
提交 radius 与 centers。每个数写成十进制字符串，例如 "0.25"。
{
"centers": [
[
"0.036771687",
"0.036771687"
],
[
"0.164152548",
"0.036771687"
],
[
"0.928437714",
"0.036771687"
],
[
"0.291533409",
"0.036771687"
],
[
"0.801056853",
"0.036771687"
],
[
"0.41891427",
"0.036771687"
],
[
"0.673675992",
"0.036771687"
],
[
"0.546295131",
"0.036771687"
],
[
"0.609985561",
"0.073543374"
],
[
"0.4826047",
"0.073543374"
],
[
"0.737366422",
"0.073543374"
],
[
"0.355223839",
"0.073543374"
],
[
"0.864747283",
"0.073543374"
],
[
"0.227842979",
"0.073543374"
],
[
"0.100462118",
"0.073543374"
],
[
"0.963228313",
"0.10156553"
],
[
"0.036771687",
"0.110315062"
],
[
"0.546295131",
"0.110315062"
],
[
"0.41891427",
"0.110315062"
],
[
"0.673675992",
"0.110315062"
],
[
"0.291533409",
"0.110315062"
],
[
"0.801056853",
"0.110315062"
],
[
"0.164152548",
"0.110315062"
],
[
"0.899537882",
"0.138337218"
],
[
"0.100462118",
"0.147086749"
],
[
"0.227842979",
"0.147086749"
],
[
"0.355223839",
"0.147086749"
],
[
"0.4826047",
"0.147086749"
],
[
"0.737366422",
"0.147086749"
],
[
"0.609985561",
"0.147086749"
],
[
"0.835847452",
"0.175108905"
],
[
"0.963228313",
"0.175108905"
],
[
"0.164152548",
"0.183858436"
],
[
"0.036771687",
"0.183858436"
],
[
"0.291533409",
"0.183858436"
],
[
"0.673675992",
"0.183858436"
],
[
"0.546295131",
"0.183858436"
],
[
"0.41891427",
"0.183858436"
],
[
"0.899537882",
"0.211880592"
],
[
"0.772157021",
"0.211880592"
],
[
"0.355223839",
"0.220630123"
],
[
"0.100462118",
"0.220630123"
],
[
"0.609985561",
"0.220630123"
],
[
"0.227842979",
"0.220630123"
],
[
"0.4826047",
"0.220630123"
],
[
"0.835847452",
"0.248652279"
],
[
"0.708466591",
"0.248652279"
],
[
"0.963228313",
"0.248652279"
],
[
"0.291533409",
"0.25740181"
],
[
"0.41891427",
"0.25740181"
],
[
"0.546295131",
"0.25740181"
],
[
"0.036771687",
"0.25740181"
],
[
"0.164152548",
"0.25740181"
],
[
"0.772157021",
"0.285423966"
],
[
"0.899537882",
"0.285423966"
],
[
"0.644776161",
"0.285423966"
],
[
"0.227842979",
"0.294173497"
],
[
"0.100462118",
"0.294173497"
],
[
"0.4826047",
"0.294173497"
],
[
"0.355223839",
"0.294173497"
],
[
"0.58108573",
"0.322195653"
],
[
"0.963228313",
"0.322195653"
],
[
"0.835847452",
"0.322195653"
],
[
"0.708466591",
"0.322195653"
],
[
"0.036771687",
"0.330945185"
],
[
"0.164152548",
"0.330945185"
],
[
"0.41891427",
"0.330945185"
],
[
"0.291533409",
"0.330945185"
],
[
"0.5173953",
"0.358967341"
],
[
"0.772157021",
"0.358967341"
],
[
"0.899537882",
"0.358967341"
],
[
"0.644776161",
"0.358967341"
],
[
"0.355223839",
"0.367716872"
],
[
"0.100462118",
"0.367716872"
],
[
"0.227842979",
"0.367716872"
],
[
"0.58108573",
"0.395739028"
],
[
"0.835847452",
"0.395739028"
],
[
"0.708466591",
"0.395739028"
],
[
"0.453704869",
"0.395739028"
],
[
"0.963228313",
"0.395739028"
],
[
"0.291533409",
"0.404488559"
],
[
"0.164152548",
"0.404488559"
],
[
"0.036771687",
"0.404488559"
],
[
"0.772157021",
"0.432510715"
],
[
"0.644776161",
"0.432510715"
],
[
"0.5173953",
"0.432510715"
],
[
"0.899537882",
"0.432510715"
],
[
"0.390014439",
"0.432510715"
],
[
"0.100462118",
"0.441260246"
],
[
"0.227842979",
"0.441260246"
],
[
"0.453704869",
"0.469282402"
],
[
"0.58108573",
"0.469282402"
],
[
"0.326324008",
"0.469282402"
],
[
"0.963228313",
"0.469282402"
],
[
"0.835847452",
"0.469282402"
],
[
"0.708466591",
"0.469282402"
],
[
"0.036771687",
"0.478031933"
],
[
"0.164152548",
"0.478031933"
],
[
"0.772157021",
"0.506054089"
],
[
"0.390014439",
"0.506054089"
],
[
"0.5173953",
"0.506054089"
],
[
"0.899537882",
"0.506054089"
],
[
"0.644776161",
"0.506054089"
],
[
"0.262633578",
"0.506054089"
],
[
"0.100462118",
"0.51480362"
],
[
"0.708466591",
"0.542825776"
],
[
"0.963228313",
"0.542825776"
],
[
"0.326324008",
"0.542825776"
],
[
"0.453704869",
"0.542825776"
],
[
"0.198943147",
"0.542825776"
],
[
"0.835847452",
"0.542825776"
],
[
"0.58108573",
"0.542825776"
],
[
"0.036771687",
"0.551575308"
],
[
"0.262633578",
"0.579597464"
],
[
"0.5173953",
"0.579597464"
],
[
"0.135252717",
"0.579597464"
],
[
"0.644776161",
"0.579597464"
],
[
"0.390014439",
"0.579597464"
],
[
"0.772157021",
"0.579597464"
],
[
"0.899537882",
"0.579597464"
],
[
"0.835847452",
"0.616369151"
],
[
"0.326324008",
"0.616369151"
],
[
"0.58108573",
"0.616369151"
],
[
"0.453704869",
"0.616369151"
],
[
"0.198943147",
"0.616369151"
],
[
"0.963228313",
"0.616369151"
],
[
"0.708466591",
"0.616369151"
],
[
"0.071562286",
"0.616369151"
],
[
"0.5173953",
"0.653140838"
],
[
"0.644776161",
"0.653140838"
],
[
"0.899537882",
"0.653140838"
],
[
"0.135252717",
"0.653140838"
],
[
"0.390014439",
"0.653140838"
],
[
"0.262633578",
"0.653140838"
],
[
"0.772157021",
"0.653140838"
],
[
"0.036771687",
"0.681162994"
],
[
"0.198943147",
"0.689912525"
],
[
"0.835847452",
"0.689912525"
],
[
"0.58108573",
"0.689912525"
],
[
"0.453704869",
"0.689912525"
],
[
"0.326324008",
"0.689912525"
],
[
"0.963228313",
"0.689912525"
],
[
"0.708466591",
"0.689912525"
],
[
"0.100462118",
"0.717934681"
],
[
"0.5173953",
"0.726684212"
],
[
"0.390014439",
"0.726684212"
],
[
"0.644776161",
"0.726684212"
],
[
"0.262633578",
"0.726684212"
],
[
"0.772157021",
"0.726684212"
],
[
"0.899537882",
"0.726684212"
],
[
"0.164152548",
"0.754706368"
],
[
"0.036771687",
"0.754706368"
],
[
"0.708466591",
"0.763455899"
],
[
"0.453704869",
"0.763455899"
],
[
"0.963228313",
"0.763455899"
],
[
"0.326324008",
"0.763455899"
],
[
"0.835847452",
"0.763455899"
],
[
"0.58108573",
"0.763455899"
],
[
"0.100462118",
"0.791478056"
],
[
"0.227842979",
"0.791478056"
],
[
"0.5173953",
"0.812484816"
],
[
"0.891045825",
"0.814936262"
],
[
"0.371009912",
"0.824504335"
],
[
"0.666764337",
"0.825816972"
],
[
"0.74338118",
"0.828183014"
],
[
"0.164152548",
"0.828249743"
],
[
"0.291533409",
"0.828249743"
],
[
"0.036771687",
"0.828249743"
],
[
"0.816656934",
"0.834451335"
],
[
"0.593620422",
"0.835923198"
],
[
"0.4453035",
"0.836517825"
],
[
"0.963228313",
"0.836999274"
],
[
"0.108954175",
"0.879730105"
],
[
"0.332542144",
"0.889298179"
],
[
"0.705142736",
"0.891003785"
],
[
"0.25916828",
"0.894288567"
],
[
"0.778418489",
"0.897272107"
],
[
"0.405523374",
"0.898373863"
],
[
"0.185748521",
"0.898550823"
],
[
"0.631998821",
"0.898658566"
],
[
"0.555722547",
"0.89895001"
],
[
"0.851942095",
"0.898977185"
],
[
"0.925476686",
"0.900113793"
],
[
"0.482188841",
"0.900142502"
],
[
"0.036771687",
"0.901793117"
],
[
"0.297565675",
"0.957012311"
],
[
"0.740692637",
"0.960402036"
],
[
"0.593596006",
"0.963191541"
],
[
"0.077198716",
"0.963228313"
],
[
"0.224285464",
"0.963228313"
],
[
"0.370845885",
"0.963228313"
],
[
"0.519988422",
"0.963228313"
],
[
"0.15074209",
"0.963228313"
],
[
"0.444389259",
"0.963228313"
],
[
"0.814181685",
"0.963228313"
],
[
"0.887725059",
"0.963228313"
],
[
"0.66720359",
"0.963228313"
],
[
"0.963228313",
"0.963228313"
]
],
"radius": "0.036771686"
}{
"n": 198
}{
"centers": [
[
"0.036771687",
"0.036771687"
],
[
"0.164152548",
"0.036771687"
],
[
"0.928437714",
"0.036771687"
],
[
"0.291533409",
"0.036771687"
],
[
"0.801056853",
"0.036771687"
],
[
"0.41891427",
"0.036771687"
],
[
"0.673675992",
"0.036771687"
],
[
"0.546295131",
"0.036771687"
],
[
"0.609985561",
"0.073543374"
],
[
"0.4826047",
"0.073543374"
],
[
"0.737366422",
"0.073543374"
],
[
"0.355223839",
"0.073543374"
],
[
"0.864747283",
"0.073543374"
],
[
"0.227842979",
"0.073543374"
],
[
"0.100462118",
"0.073543374"
],
[
"0.963228313",
"0.10156553"
],
[
"0.036771687",
"0.110315062"
],
[
"0.546295131",
"0.110315062"
],
[
"0.41891427",
"0.110315062"
],
[
"0.673675992",
"0.110315062"
],
[
"0.291533409",
"0.110315062"
],
[
"0.801056853",
"0.110315062"
],
[
"0.164152548",
"0.110315062"
],
[
"0.899537882",
"0.138337218"
],
[
"0.100462118",
"0.147086749"
],
[
"0.227842979",
"0.147086749"
],
[
"0.355223839",
"0.147086749"
],
[
"0.4826047",
"0.147086749"
],
[
"0.737366422",
"0.147086749"
],
[
"0.609985561",
"0.147086749"
],
[
"0.835847452",
"0.175108905"
],
[
"0.963228313",
"0.175108905"
],
[
"0.164152548",
"0.183858436"
],
[
"0.036771687",
"0.183858436"
],
[
"0.291533409",
"0.183858436"
],
[
"0.673675992",
"0.183858436"
],
[
"0.546295131",
"0.183858436"
],
[
"0.41891427",
"0.183858436"
],
[
"0.899537882",
"0.211880592"
],
[
"0.772157021",
"0.211880592"
],
[
"0.355223839",
"0.220630123"
],
[
"0.100462118",
"0.220630123"
],
[
"0.609985561",
"0.220630123"
],
[
"0.227842979",
"0.220630123"
],
[
"0.4826047",
"0.220630123"
],
[
"0.835847452",
"0.248652279"
],
[
"0.708466591",
"0.248652279"
],
[
"0.963228313",
"0.248652279"
],
[
"0.291533409",
"0.25740181"
],
[
"0.41891427",
"0.25740181"
],
[
"0.546295131",
"0.25740181"
],
[
"0.036771687",
"0.25740181"
],
[
"0.164152548",
"0.25740181"
],
[
"0.772157021",
"0.285423966"
],
[
"0.899537882",
"0.285423966"
],
[
"0.644776161",
"0.285423966"
],
[
"0.227842979",
"0.294173497"
],
[
"0.100462118",
"0.294173497"
],
[
"0.4826047",
"0.294173497"
],
[
"0.355223839",
"0.294173497"
],
[
"0.58108573",
"0.322195653"
],
[
"0.963228313",
"0.322195653"
],
[
"0.835847452",
"0.322195653"
],
[
"0.708466591",
"0.322195653"
],
[
"0.036771687",
"0.330945185"
],
[
"0.164152548",
"0.330945185"
],
[
"0.41891427",
"0.330945185"
],
[
"0.291533409",
"0.330945185"
],
[
"0.5173953",
"0.358967341"
],
[
"0.772157021",
"0.358967341"
],
[
"0.899537882",
"0.358967341"
],
[
"0.644776161",
"0.358967341"
],
[
"0.355223839",
"0.367716872"
],
[
"0.100462118",
"0.367716872"
],
[
"0.227842979",
"0.367716872"
],
[
"0.58108573",
"0.395739028"
],
[
"0.835847452",
"0.395739028"
],
[
"0.708466591",
"0.395739028"
],
[
"0.453704869",
"0.395739028"
],
[
"0.963228313",
"0.395739028"
],
[
"0.291533409",
"0.404488559"
],
[
"0.164152548",
"0.404488559"
],
[
"0.036771687",
"0.404488559"
],
[
"0.772157021",
"0.432510715"
],
[
"0.644776161",
"0.432510715"
],
[
"0.5173953",
"0.432510715"
],
[
"0.899537882",
"0.432510715"
],
[
"0.390014439",
"0.432510715"
],
[
"0.100462118",
"0.441260246"
],
[
"0.227842979",
"0.441260246"
],
[
"0.453704869",
"0.469282402"
],
[
"0.58108573",
"0.469282402"
],
[
"0.326324008",
"0.469282402"
],
[
"0.963228313",
"0.469282402"
],
[
"0.835847452",
"0.469282402"
],
[
"0.708466591",
"0.469282402"
],
[
"0.036771687",
"0.478031933"
],
[
"0.164152548",
"0.478031933"
],
[
"0.772157021",
"0.506054089"
],
[
"0.390014439",
"0.506054089"
],
[
"0.5173953",
"0.506054089"
],
[
"0.899537882",
"0.506054089"
],
[
"0.644776161",
"0.506054089"
],
[
"0.262633578",
"0.506054089"
],
[
"0.100462118",
"0.51480362"
],
[
"0.708466591",
"0.542825776"
],
[
"0.963228313",
"0.542825776"
],
[
"0.326324008",
"0.542825776"
],
[
"0.453704869",
"0.542825776"
],
[
"0.198943147",
"0.542825776"
],
[
"0.835847452",
"0.542825776"
],
[
"0.58108573",
"0.542825776"
],
[
"0.036771687",
"0.551575308"
],
[
"0.262633578",
"0.579597464"
],
[
"0.5173953",
"0.579597464"
],
[
"0.135252717",
"0.579597464"
],
[
"0.644776161",
"0.579597464"
],
[
"0.390014439",
"0.579597464"
],
[
"0.772157021",
"0.579597464"
],
[
"0.899537882",
"0.579597464"
],
[
"0.835847452",
"0.616369151"
],
[
"0.326324008",
"0.616369151"
],
[
"0.58108573",
"0.616369151"
],
[
"0.453704869",
"0.616369151"
],
[
"0.198943147",
"0.616369151"
],
[
"0.963228313",
"0.616369151"
],
[
"0.708466591",
"0.616369151"
],
[
"0.071562286",
"0.616369151"
],
[
"0.5173953",
"0.653140838"
],
[
"0.644776161",
"0.653140838"
],
[
"0.899537882",
"0.653140838"
],
[
"0.135252717",
"0.653140838"
],
[
"0.390014439",
"0.653140838"
],
[
"0.262633578",
"0.653140838"
],
[
"0.772157021",
"0.653140838"
],
[
"0.036771687",
"0.681162994"
],
[
"0.198943147",
"0.689912525"
],
[
"0.835847452",
"0.689912525"
],
[
"0.58108573",
"0.689912525"
],
[
"0.453704869",
"0.689912525"
],
[
"0.326324008",
"0.689912525"
],
[
"0.963228313",
"0.689912525"
],
[
"0.708466591",
"0.689912525"
],
[
"0.100462118",
"0.717934681"
],
[
"0.5173953",
"0.726684212"
],
[
"0.390014439",
"0.726684212"
],
[
"0.644776161",
"0.726684212"
],
[
"0.262633578",
"0.726684212"
],
[
"0.772157021",
"0.726684212"
],
[
"0.899537882",
"0.726684212"
],
[
"0.164152548",
"0.754706368"
],
[
"0.036771687",
"0.754706368"
],
[
"0.708466591",
"0.763455899"
],
[
"0.453704869",
"0.763455899"
],
[
"0.963228313",
"0.763455899"
],
[
"0.326324008",
"0.763455899"
],
[
"0.835847452",
"0.763455899"
],
[
"0.58108573",
"0.763455899"
],
[
"0.100462118",
"0.791478056"
],
[
"0.227842979",
"0.791478056"
],
[
"0.5173953",
"0.812484816"
],
[
"0.891045825",
"0.814936262"
],
[
"0.371009912",
"0.824504335"
],
[
"0.666764337",
"0.825816972"
],
[
"0.74338118",
"0.828183014"
],
[
"0.164152548",
"0.828249743"
],
[
"0.291533409",
"0.828249743"
],
[
"0.036771687",
"0.828249743"
],
[
"0.816656934",
"0.834451335"
],
[
"0.593620422",
"0.835923198"
],
[
"0.4453035",
"0.836517825"
],
[
"0.963228313",
"0.836999274"
],
[
"0.108954175",
"0.879730105"
],
[
"0.332542144",
"0.889298179"
],
[
"0.705142736",
"0.891003785"
],
[
"0.25916828",
"0.894288567"
],
[
"0.778418489",
"0.897272107"
],
[
"0.405523374",
"0.898373863"
],
[
"0.185748521",
"0.898550823"
],
[
"0.631998821",
"0.898658566"
],
[
"0.555722547",
"0.89895001"
],
[
"0.851942095",
"0.898977185"
],
[
"0.925476686",
"0.900113793"
],
[
"0.482188841",
"0.900142502"
],
[
"0.036771687",
"0.901793117"
],
[
"0.297565675",
"0.957012311"
],
[
"0.740692637",
"0.960402036"
],
[
"0.593596006",
"0.963191541"
],
[
"0.077198716",
"0.963228313"
],
[
"0.224285464",
"0.963228313"
],
[
"0.370845885",
"0.963228313"
],
[
"0.519988422",
"0.963228313"
],
[
"0.15074209",
"0.963228313"
],
[
"0.444389259",
"0.963228313"
],
[
"0.814181685",
"0.963228313"
],
[
"0.887725059",
"0.963228313"
],
[
"0.66720359",
"0.963228313"
],
[
"0.963228313",
"0.963228313"
]
],
"radius": "0.036771686"
}提交 radius 与 centers。每个数写成十进制字符串，例如 "0.25"。 · 验证器 v1.0.0
聊思路、贴方法、问为什么卡住。所有登录用户都可以发帖；发言公开署名，与纪录使用同一个名字，署名后的 #编号是账号注册序号，冒不了名。新发言经自动审核后公开。
按选手与子题分组，默认展示最新一篇。历史笔记及回复完整保留，点击笔记可查看和回复。笔记随纪录提交发布。